The line would run as far as Edinburgh and Glasgow via Birmingham and Manchester.
Director at Arup Mark Bostock said: “The proposal to link Heathrow into the rail network would enable people travelling from some of Heathrow's principal markets to arrive at the airport by train.
“Moreover, these plans fit in with emerging proposals to extend high speed rail lines north. Looking to the future, we could see travel times from Heathrow to Leeds and Manchester by rail reduced to less than two hours."
Arup's proposal would also see Heathrow become the first stop on an extended high speed rail network that currently terminates at King's Cross St Pancras, which would link the airport directly with continental Europe.
The consultant has been in talks with BAA, airlines, local councils and Government about the plans.
Part of the work involved identifying more than 22 potential sites for the new terminal and settled on an area approximately 3km north of the existing T5.